3 problems

Let $\mu$ and $\mu'$ be offspring distributions satisfying … with $1<\alpha\leq\alpha'<2$ and $c,c'>0$, and let $\tau_n$ and $\tau'_n$ be the corresponding conditioned random trees…

Let the node weights of an inhomogeneous random graph or a configuration-model graph follow a distribution with a power-law tail of parameter $4 > \alpha > 3$, and assign i.i.d. ca…

Durrett's conjecture. The largest component of $G_n$ is of order